The connected_components() functions compute the connected
components of an undirected graph using a DFS-based approach. A
connected component of an undirected graph is a set of
vertices that are all reachable from each other. If the connected
components need to be maintained while a graph is growing the
disjoint-set based approach of function incremental_components() is faster. For ``static'' graphs
this DFS-based approach is faster [8].

The output of the algorithm is recorded in the component property map
comp, which will contain numbers giving the component number
assigned to each vertex. The total number of components is the return
value of the function.

Parameters

The algorithm computes how many connected components are in the graph,
and assigning each component an integer label. The algorithm then
records which component each vertex in the graph belongs to by
recording the component number in the component property map. The
ComponentMap type must be a model of Writable Property
Map. The value type shouch be an integer type, preferably the same
as the vertices_size_type of the graph. The key type must be
the graph's vertex descriptor type.Python: Must be an vertex_int_map for the graph.Python default: graph.get_vertex_int_map("component")

Named Parameters

UTIL: color_map(ColorMap color)

This is used by the algorithm to keep track of its progress through
the graph. The type ColorMap must be a model of Read/Write
Property Map and its key type must be the graph's vertex
descriptor type and the value type of the color map must model
ColorValue.Default: an
iterator_property_map created from a
std::vector of default_color_type of size
num_vertices(g) and using the i_map for the index
map.Python: The color map must be a vertex_color_map for
the graph.

IN: vertex_index_map(VertexIndexMap i_map)

This maps each vertex to an integer in the range [0,
num_vertices(g)). This parameter is only necessary when the
default color property map is used. The type VertexIndexMap
must be a model of Readable Property
Map. The value type of the map must be an integer type. The
vertex descriptor type of the graph needs to be usable as the key
type of the map.Default:get(vertex_index, g).
Note: if you use this default, make sure your graph has
an internal vertex_index property. For example,
adjacenty_list with VertexList=listS does
not have an internal vertex_index property.Python: Unsupported parameter.

Complexity

The time complexity for the connected components algorithm is also
O(V + E).